Local Descriptions of Roots of Cubic Equations over P-adic Fields

الأصل · EN

The most frequently asked question in the p-adic lattice models of statistical mechanics is that whether a root of a polynomial equation belongs to domains Zₚ*, Zₚₚ*, Zₚ, Qₚₚ*, Qₚ(Zₚₚ*), Qₚₚ, Qₚ or not. However, this question was open even for lower degree polynomial equations. In this paper, we give local descriptions of roots of cubic equations over the p-adic fields for p>3.